Recirculating adder



Nov. 3, 1964 Filed 001'.. 2, 1961 F. C. CHIANG RECIRCULATING ADDER FIG- l Fim/:Lw C', Cif/ANG Nov. 3, 1964 F. C. CHIANG RECIRCULATING ADDER Filed Oct. 2. 1961 l0 Sheets-Sheet 2 N0V- 3, 1964 F. c. cHlANG 3,155,822

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RECIRCULATING ADDER United States Patent O 3,155,822 RECIRCULATING ADDER Franklin C. Chiang, Palo Alto, Calif., assigner to International Control Machines of Santa @lara County, Mountain View, Calif., a corporation of Caiifornia Fiied Get. 2, 1961, Ser. No. 142,398 l Ciaims. (Cl. 23S- 173) This invention relates to high-speed electric adding and subtracting circuits, and particularly to recirculating adders for performing any number of successive additions and subtractions, accumulating the sums and dilerences, and automatically entering the latest subtotal as the augend or minuend for the next addition or subtraction.

Adders according to this invention incorporate augend entry circuits and addend entry circuits, each having memory provisions for temporary storage of the numbers to be added. (Subtraction is performed by adding the complement of the subtrahend, as hereinafter explained.) The augend and addend entry circuits are interconnected with a plurality of delay circuits, in such a way that the sum or diierence of the stored numbers is translated into a time position of an electric pulse relative to a train of other pulses. This is decoded by coincidence means, and the subtotal is entered into the memory provisions of the augend entry circuit in preparation for the next addition or subtraction. Preferred arrangements for performing the necessary carry functions, clearing the memory provisions, and the like, are included in the exempiary embodiments hereinafter described.

@ne advantage of the recirculating adders provided by this invention is that they are easily adapted to any radix desired-the specific embodiments illustrated and described have been designed for radix ten. The modiiications necessary to accommodate any other radix desired will be apparent to those skilled in the art. Another advantage is high speed-logic functions are performed by inherently fast-acting delay lines and gates, While inherently slower components, such as hip-flops, are employed only in the memory provisions where speed requirements are less severe. The flip-flops only need to have a rise-time equal to or less than the spacing between number pulses on the delay line. Still other advantages are compactness, reliability and economy resulting from the simplicity of circuitry relative to the operations performed.

The foregoing and other aspects and advantages of the invention may be better understood from the following illustrative description and the accompanying drawings. The scope of the invention is pointed out in the appended claims.

FIG. l is a schematic block diagram of a six-stage recirculating adder embodying principles of this invention, the six stages being essentially identical, there being one stage for each digit in a six-digit number of radix lil.

FIG. 2 is a schematic block diagram of a single stage of the adder shown in FIG. l, various parts represented by blocks in FiG. 2 being more fully illustrated in FIGS. 3-l0, as indicated.

FIG. 3 is a schematic circuit diagram of the nineteenunit delay circuit Sil of FiG. 2.

FIG. 4 is a schematic block and circuit diagram of the augend entrycircuit tu of FIG. 2.

FIG. 5 is a schematic block and circuit diagram of the carry entry circuit 5th of FIG. 2.

FG. 6 is a schematic block and circuit diagram of the nine-unit delay circuit du of FIG. 2. f

FIG. 7 is a schematic block and circuit diagram ofthe addend entry circuit 7b of FIG. 2.

FIGS. 8A and 8B together constitute aschematic block .and circuit diagram' of the sum decoder circuit Si) of ice 2 FIG. 2, the right end of FIG. 8A connecting directly to the left end oi FIG. 8B.

FIG. 9 is a schematic block and circuit diagram of the transfer circuit of FIG. 2.

FIG. l0 is a schematic circuit diagram of the readout circuit 169 of FIG. 2.

FIG. ll is a schematic block diagram illustrating an alternative adder stage incorporating the subcircuits illustrated in FIGS. 3, 5, 6, 7 and 8, together with an alternative augend entry and readout circuit 120, the parts being arranged somewhat differently and cooperating in a different manner from the stage shown in FIG. 2.

FG. 12 is a schematic block and circuit diagram of the augend entry and readout circuit 12u of FIG. 1l.

In a number of instances, duplicate parts are provided in the apparatus illustrated for electric signals representing different numerals-eg., the ten digits zero to nine are entered into the addend entry circuit 7b of each stage by means of electric signals through ten identical, parallel leads. For convenience of reference, these ten leads are all represented by the reference number 2t), followed by a parenthesis containing the numeral representedthat is, the lead for entering addend digit zero is identified by reference number 20GB), the lead for entering addend digit one is identied by reference number 20(1), etc. The group of ten parallel leads as a Whole is identied by reference number 20GB-9), The same reference nurnber system has been employed throughout the drawings. Also, parts that are best shown in FIG. 2 are identitied by reference numbers 2u et seq., those best shown in FIG. 3 are identiiied by reference numbers 3i) et seq., etc. Leads extending from parts in one iigure to parts in another figure are numbered according to the figure in which they originate.

Conventional and-gates, or-gates, amplifiers, flip-flops, blocking oscillators, differentiating circuits, a pulse generator, a constant-current supply, and a printer are represented only by blocks, these conventional components being so well known to those skilled in the art that no further description is necessary. Numerous circuit variations and equivalents for these conventional components are also known and may be used. It will be understood that an and-gate provides a signal at its output lead only when signals are received at all of its input leads concurrently, and that an or-gate provides a signal at its output lead when a signal is applied to any of its input leads. A blocking oscillator provides an output pulse of lixed amplitude and duration Whenever it is triggered by an input pulseit can be replaced by equivalents, such as a one-shot multivibrator, or, in some cases, an arnplier.

The six-stage recirculating adder illustrated in FIG. l is designed to operate in the familiar decimal number system, i.e., radix ten, to receive successive addend and subtrahend entries of up to five digits each, and to ac cumulate totals of up to six digits. Thus, the iirst register or stage, identied by reference number lll-2, may accept and register the hundredths digits (or cents), the second stage liu-1 may accept and Yregister the tenths digits (dimes), the third stage ill may accept and register the units digits (dollars), the fourth stage itil may accept and register the tens digits, the fifth stage 102 may accept and register the hundreds digits, and thesixth stage 103 may accept and register the thousands digits.

Each of the iirst ve registers or stages is provided with a group of ten (equal to the radix) parallel leads 2tl(j9) that serve as a ten-digit parallel entry for receiving electric signals representing the ten digits zero to nine that are to be added or subtracted from the latest augend vor subtotal digit previously `accumulated in that register.

Whenever a digit must be carriedirom one stage to the` next, an electric signal is transmitted from a lead 21 of the stage in which the carry originates to the carry entry lead 22 of the next stage.

The six registers are so arranged that any live-digit number entered through the live groups of leads 2tl(0*9) will be added to the previously accumulated subtotal, unless an electric signal is concurrently supplied through the subtract order entry leads 23. As is more fully explained hereinafter, entry of a subtract order through leads 23 causes each register to add to the previously accumulated subtotal digit the difference between the number nine (one less than the radix ten) and the digit entered through leads 29(0-9). Concurrently with the subtract order entry, a carry signal is entered through lead 22 of the first stage itl-2, and the digit nine (one less than the radix) is entered through lead (9) or the last stage 103, by means of the connections shown in FG. l. As a result, a subtract order entry causes the six-stage adder to add to the last previous subtotal the complement of the five-digit number concurrently entered through the five groups of leads 20(0-9).

For resetting the accumulated total to zero, an electric signal is supplied through the reset order entry leads 2&3 into each ofthe six stages.

The six stages of the adder preferably are identical, with the exception that parts associated with the unused entry leads 26(0-8) and 23 of the last stage 193, and the unused carry output provisions of the last stage, may be omitted from that stage of economy. Also, it so desired, duplicate components, particularly pulse generator 25 and ninetee -unit delay circuit 3l), may be combined into a common unit shared by all six stages. Otherwise, each of the six stages preferably conforms to the block diagram illustrated in FIG. 2.

Referring to FIG. 2, a pulse generator 25 periodically supplies an electric pulse through lead 26 to a delay circuit 3i), which provides trains of pulses following one another at equal intervals of one time unit. One time unit may be any convenient period, e.g., one niicrosecond. The total delay provided by circuit 30, expressed in the chosen time units, is at least equal to twice the radix minus two (e.g., 2X lil-2:18), and preferably is more, for reasons hereinafter explained. In the illustrated embodiment, circuit 36 provides a total delay of nineteen units. The pulse width, or duration, of the pulses supplied by generator 25 should be less than one time unit, and the pulse repetition period should be greater than the total nineteen-unit delay of circuit 30. Each pulse supplied through lead 26 initiates a new operating cycle. At least two such cycles should be available for each addition or subtraction; hence, the repetition period of the pulses supplied by generator 25 should be longer than one-half the minimum period between the entry through leads 26(9-9) of successive numbers to be added or subtracted.

A group of ten leads 31(0-9) leads from delay circuit 3i) to the augend entry circuit 49. Responsive to each pulse received through lead 26, delay circuit 3d supplies a pulse to cach of the ten (equal to the radix) leads 31(t9) in succession, at intervals of one time-unit. In other words, approximately immediately after receiving a pulse through lead 25, circuit 3d transmits a pulse through lead 31(0) to circuit 4t); one unit of time later circuit 33 transmits a pulse through lead 31(1) to circuit 4i); etc.

A group of nineteen (one less than twice the radix) leads 32(t)-18) connects delay circuit 39 to a sum decoder circuit 89, and responsive to each input pulse received through lead 26, delay circuit Sil transmits an electric pulse through each of the leads 32(0-18) in succession, at one-unit time intervals. For reasons that will become apparent as the description proceeds, it is preferable to provide a delay between the Vpulse transmitted through lead 31(6) and the pulse transmitted through lead 32(0). In the illustrated embodiment, this delay is one unit; hence a pulse is transmitted through lead 32(6) concurrently with the transmission of a pulse through lead 31(1),

that is, approximately one time-unit after delay circuit 34B receives a pulse through lead 26. One time-unit after the pulse through lead 32(0), a pulse is transmitted through lead 32(1); and another time-unit later, a pulse is transmitted through lead 32(2); etc. rthus, there is a delay of nineteen time-units between the receipt of a pulse through lead 26 and transmission of the pulse through lead 32(18), and a nineteen-unit delay circuit is employed.

Digits entered in the augend entry circuit 40, as hereinafter explained, control connection of `a selected one of the leads 31(9-9) to a lead 41, which connects circuit 4G to a carry entry circuit dil and also to a transfer circuit 93. Thus, if the digit zero is stored in the memory provisions of augend entry circuit 4t), a pulse is transmitted from lead 3&9) to lead 41 approximately immediately following the receipt of a pulse by delay circuit 30 through lead 26. 1i the digit one is stored in the augend entry circuit, then the pulse from lead 31(1) is transmitted to lead 41, etc. Hence, for each increase of one in the numerical value of the digit stored in augend entry circuit 4%, the transmission of a pulse to lead 41 is delayed by one timeunit relative to the pulse supplied through lead 26 by the pulse generator, and the time position or the pulses transmitted through lead 41 is representative of the subtotal digit stored in the memory provisions of the augend entry circuit 40.

Responsive to each pulse transmitted through lead 41, carry entry circuit 50 transmits a pulse either through lead Si or through lead 52, depending upon whether or not a carry digit has been stored in the memory provisions of carry entry circuit itl. For reasons that will become clear as the description proceeds, the carry entry circuit provides a delay of approximately two time-units between the receipt of a pulse through lead and the transmission of a pulse through lead Si when there is a carry digit to be added. When there is no carry digit to be added, circuit 'tl provides a delay of approximately one time-unit between the receipt of a pulse through lead 41 and the transmission of a pulse through lead 52.

Responsive to each pulse transmitted through lead 52, a nine-unit delay circuit 66 transmits pulses through each of the ten (equal to the radix) leads 61(49-0) in succession at intervals of one time-unit. Each unit of delay provided by circuit 6l) is equal to one unit of the delay provided by circuit 3l?, and the total number of delay units provided by circuit 60 is one less than the radix. It no subtract order entry has been received through lead 23, then a pulse is transmitted through the ten leads 61(9-9) successively in direct numerical order, i.e., a pulse is transmitted through lead 61(9) approximately immediately following the receipt of a pulse through lead 52, a pulse is transmitted through lead 61(1) one timeunit later, etc. if a subtract order entry has been received through lead 23, delay circuit 60 transmits pulses through leads 61(9-9) successively in inverse numerical order, i.e., transmits a pulse through lead 61(9) almost immediately after receipt ci' a pulse through lead 52, transmits a pulse through lead 61(8) one time-unit later, etc.

The addend (or subtrahend) digit is entered into the memory provisions of addend entry circuit 70 through the ten parallel leads 253634)). lf the digit stored in the addend entry circuit is zero, a pulse is transmitted through lead 71 to or-gate 27 approximately immediately after receipt of a pulse through lead 51GB). lr" the digit stored in the addend entry circuit is one, then a pulse is transmitted through lead 71 approximately immediately following receipt of a pulse through lead 61(1), and so forth. Thus, in the case of addition, the pulse transmitted through lead 71 is delayedrelatives to the pulse transmitted through lead 52 by a member ot timeunits corresponding to the digit stored in the memory provisions of addend entry circuit 7d. In the case of subtraction, the delay in time-units is equal to the difference between nine (one less than the radix) and the stored subtrahend digit. Upon receipt of a pulse through either of the leads 5l or 7l, or-gate 27 transmits a pulse through lead 28 to sum decoder circuit S0.

From the foregoing description it will be seen that the pulse transmitted through lead 28 is delayed, relative t0 the pulse supplied through lead 26 by the pulse generator, by an amount equal to the sum of several delays: a first delay of a number of time-units equal to the digit stored in augend entry circuit di); and a second delay of two time-units in circuit Si) if there is a carry digit to be added; or, if there is no carry digit to be added, a second delay of one time-unit in circuit Si) and a third delay of a number of time-units equal either (in the case of addition) to the digit stored in addend entry circuit '70 or (in the case of subtraction) to nine minus the digit stored in addend entry circuit 70. Two points will be noted: carry digits and addend digits are added in separate operating cycles; in each cycle, the total delay is one time-unit larger than the required sum of the digits to be added, or difference between the digits to be subtracted. Hence, if the required sum or difference is zero, the leading edge of the pulse transmitted through lead 2S will be coincident with the pulse transmitted through lead 32(0)-in this case, decoder circuit Si? will transmit a pulse through lead 81(0) to the transfer circuit 90. If the required sum or difference is one, the leading edge of the pulse through lead 28 will be coincident with the pulse through lead 32(1), and the sum decoder circuit will transmit a pulse through lead 8l(l) to transfer circuit 99. In this way, decoder circuit El) transmits a pulse through the proper one of ten (equal to the radix) leads 8109-9) to transfer circuit 9b responsive to every pulse received through lead 28 having a time position representing a sum or difference number smaller than ten (the radix selected).

If the sum or difference is ten or more, the sum decoder circuit S0 supplies a carry pulse to the next stage through lead 2l, and also supplies, through the proper one of leads 81(0-9), a pulse representing the new subtotal digit to be accumulated in augend entry circuit et), i.e., the sum or difference number minus the radix ten. Circuitry whereby this may be accomplished is illustrated in FIGS. 8A and 8B, hereinafter described.

As is more fully explained hereinafter, transfer circuit 9i) has memory provisions for storing any one of the ten digits zero to nine. Pulses supplied from the augend entry circuit 40 through lead 4l act to clear the previously stored digit from transfer circuit 90. Pulses through any one of the ten leads Slw-El) from sum decoder circuit Si) act to store a new digit in transfer circuit 90. There is always at least one unit of delay between the occurrence of a pulse on lead 4l and a pulse on any of the leads 31(8-9). Therefore, there can be no interference between the initiation of a clearing operation and an entry operation. If the clearing operation has not been completed before the entry pulse is received over a lead Sidi-9), this is of no consequence, because following operating cycles (each initiated by a pulse from generator 2S) will cause repeated pulses through the same one of the leads 81(0-9) until the sum digit is actually entered into the transfer circuit 9b.

Once the new digit has been entered in transfer circuit 9i), a pulse is supplied through the three branches of lead 92 to the augend entry circuit lll?, the carry entry circuit 50, and the addend entry circuit 70. This pulse clears the previous subtotal digit from the memory provisions of augend entry circuit dil. lf the addition yof a carry has been accomplished, the pulse through lead 92 clears the stored carry digit from the memory provisions of carry entry circuit Si), so that the digit, if any, stored in addend entry circuit 7b can be added to, or subtracted from, the accumulated subtotal in the next operating cycle. If the digit stored in addend entry circuit 7l) has been added to the subtotal, then the pulse supplied 6 through lead 92, signifying entry of the new subtotal digit into transfer circuit @0, clears the memory provisions of the addend entry circuit so that it may accept the next digit to be added or subtracted.

While a digit is stored in the memory provisions of transfer circuit 9h, an electric signal is supplied continuously through the proper one of ten (equal to the radix) leads 91(9-9) to the augend entry circuit 4). It will be noted, as the description proceeds, that the augend entry circuit can not supply another pulse through lead 41 until the new subtotal digit has been successfully entered. After the new subtotal is entered in circuit 40, the next operating cycle will provide a pulse through lead 41 which will clear the memory provisions of transfer circuit 90.

The adder described can operate with extreme rapidity--a complete live-digit addition or subtraction may take only a few microsseconds. Hence, the time between receipt of an addend or subtrahend digit through leads Zimt-9) and entry of the new subtotal digit in augend entry circuit 4@ is practically negligible. The new subtotal digit remains stored in augend entry circuit 4l) until receipt of a further entry for addition or subtraction. Hence, except for practically negligible intervals following the receipt of each new entry, the latest accumulated subtotal digit is continuously stored in augend entry circuit 40. The identity of this stored subtotal digit is indicated by an electric signal supplied through the proper one of ten leads 2W-9) to a readout circuit llliil.

Referring to FIG. 3, the ninteen-unit delay circuit 39 comprises a delay line 33 provided with twenty equally spaced terminals: two end terminals and eighteen taps. Lead 26 connects to one of the end terminals for supplying pulses from generator 25 into one end of the delay line 33. The other end terminal of the delay line is connected to a resistor 34, which terminates the delay line in its characteristic impedance, so that pulses reaching the far end of the delay line will be mostly absorbed and not reflected. The delay line is so constructed that the time required for a pulse to travel the entire length of the delay line is exactly nineteen of the chosen time-units, while the interval between the appearance of this pulse at one terminal of the line and its appearance at lthe next following terminal is exactly one time-unit.

Lead 3l(0) is connected to the input end terminal of the delay line; thus, a pulse is transmitted through lead 31(6) to the augend entry circuit almost immediately following the receipt of each pulse from the pulse generator through lead 2d. Leads 31(1-9) are connected as shown, in numerical order, to the first nine taps of the delay line, so that a pulse is transmitted through lead 31(1) after a delay of one time-unit, a pulse is transmitted through lead 31(2) after a delay of two time-units, etc. Leads 32(0-l7) are connected as shown, in numerical order, to the eighteen taps of delay line 33, and lead 32(l8) is connected to the end terminal of the delay line opposite the input end. Thus, responsive to each pulse supplied through lead 26, a pulse istransmitted,

through lead 32(il) after a delay of one time-unit, a pulse is transmitted through lead 32(l) after a delay of two time-units, etc. The pulse transmitted through lead 32(18) has the maximum time delay of nineteen timeunits.

The augend entry circuit 40 is shown in FIG. 4. AsV hereinbefore explained, delay circuit 30 supplies a pulse, through each of the leads 31(09) at one time-unitv intervals during each operating cycle initiated by a pulse from generator 25. The memory provisions of the augend entry circuit consists of ten flip-flops 43(0f9), one for each of the ten digits zero to nine Vof the chosen number system. vConnected between these ip-ops and the ten leads 31(0-9) are ten and-gates y44(0-9), arranged as shown. Each and-gate has one input lead connected to one Iof the leads 31(4)-9), another input lead connected to an output lead of the corresponding one of the flipflops 43(0-9), and an output lead connected, in common with the output leads of the other nine and-gates 44, to the input of a blocking oscillator 47. So long as a digit is stored in any one of the flip-iiops 43(0-9), that flipilop transmits a signal to one input lead of the corresponding one of the and-gates 44(0-9), and, when a pulse is received through the corresponding one of leads 31(0-9), the selected and-gate transmits a pulse through its output lead to trigger blocking oscillator 47.. .The blocking oscillator generates a pulse having a duration of at least ten time-units. Thus, under no circumstances can oscillator 47 be triggered more than once during a single operating cycle. Dilereutiating circuit 48 forms a relatively short pulse, having a duration no greater than one time-unit, at the leading edge of the longer pulse generated by the blocking oscillator. The short pulse is transmitted through lead 41 to the carry entry circuit 5G and the transfer circuit 90.

And-gates connected to flip-flops in which no digit is stored do not transmit pulses to their output leads; hence, if there is no digit stored in the ilip-fiops 4301-9), no pulse will be transmitted through lead 41 to the carry cntry circuit and the transfer circuit. If a single digit is stored in the flip-flops 43(0-9), a single pulse in each operating cycle will be transmitted from the corresponding one of the leads 31(0-9) through the corresponding and-gate 44(0-9) to blocking oscillator 47, which will operate to send a pulse through differentiating circuit 4S to lead 41. Thus, there is provided at lead 41 a pulse having a time position, relative to the initiating pulse supplied through lead 26, that is representative of the digit stored in augend entry circuit 40. In the embodiment illustrated, this time position corresponds to a delay of a number of time-units equal to the stored augend digit. If two digits should inadvertently become stored in flip-flops 43(0-9) concurrently, two pulses would be transmitted to oscillator 47, but only the first would trigger the blocking oscillator. Thus, no more than one pulse per cycle (of effective polarity to operate following components) will be transmitted through lead 41 under any circumstances.

Reset terminals of the ten dip-flops 43(0-9) are connected in parallel to lead 92, so that all flip-flops are reset-i.e., triggered to the state which cuts olf all ten of the and-gates 44(0-9)-whenever a pulse is received through lead 92 from the transfer circuit 90. Thus, the previously stored digit is immediately cleared from the memory of the augend entry circuit upon entry of a new subtotal digit in transfer circuit 90.

While the new subtotal digit is stored in transfer circuit 90, an electric signal is supplied continuously through the corresponding one of leads 91(0-9). The ten leads 940-9) are connected to input leads of ten and-gates 45(0-9). Each of the last mentioned and-gates has a second input lead connected to the lead 31(0), so that a pulse is supplied to the second input lead of and-gates 45(0-9) at the beginning of each operating cycle initiated by a pulse from generator 2S. Whenever a digit is stored in transfer circuit 90, one of the and-gates 45(0-9) will receive signals at both its inputs when the pulse arrives from lead 31(0), and at this instant will transmit a pulse through its output lead to an input terminal of the proper one of Hip-flops 43(0-9) to store the new subtotal digit in the memory of the augend entry circuit. As has already been noted, no pulse will be transmitted through lead 41 until the new subtotal digit is successfully stored in one of the flip-flops 43(0-9), and transfer circuit 9i) continues to supply a signal through the appropriate one of leads 91(0-9) until the transfer circuit is reset by the receipt of a pulse through lead 41. Thus, operation is completely reliable, whether entry of the new digit into the augend entry circuit is completed in one operating cycle or not.

The ten leads 42(G9) are connected to the outputs of the ten nip-flops 43 (0 9), so that an output signal is supplied substantially continuously to readout circuit 190 through the lead 42(0-9) that corresponds to the digit stored in the augend entry circuit.

The carry entry circuit 50 is so arranged that a carry digit will be added to the accumulated subtotal digit whenever an electric pulse representing a carry has been received from the preceding stage through lead 22. In the illustrated embodiment, the addition of carry digits takes precedence over addition of digits received through leads 20(6-9), the carry digit, if any, being added in one operating cycle, and the digit stored in circuit 70 being added or subtracted in a following operating cycle.

Referring to FIG. 5, illustrating the carry entry circuit, lead 41 is connected to two branch circuits, containing and-gates 53 and 54 controlled by a flip-flop 55 so that pulses received through lead 44 will be transmitted through only one of the two and-gates 53 and 54. Lead 22 is connected to one input of ip-tlop 55, which acts as a memory for storing the carry digits received from the preceding stage. Input leads of gates S3 and 54 are connected to opposite outputs of Hip-flop 55, as indicated in the drawing in such a manner that gate 53 will transmit pulses from lead 41 only when a carry digit is stored in Hip-ildp 55 and gate 54 will transmit pulses from lead 41 only when no carry digit is stored in ilip-ilop 55. The other input lead of gate 53 is connected directly to lead 41 and the other input lead of gate 54 is connected to lead 41 through a preferably adjustable, approximately one time-unit delay circuit 56. The output of gate 54 is connected to lead 52 for supplying pulses to the nineunit delay circuit 6i) when there is no carry digit to be added. Delay line 56 supplies the approximately one unit of delay required for the pulse through lead 28 to reach sum decoder circuit simultaneously with the pulse through lead 32(0), when both augend and addend digits are zero. Delay unit S6 is preferably made adjustable to permit compensation for any differences between the unavoidable delays encountered elsewhere in the circuits, so that precise time coincidence of the proper pulses can be obtained at the sum decoder circuit.

When there is a carry digit stored in flip-flop 55, andgate 54 will not transmit pulses, but and-gate 53 will transmit pulses from lead 41 through a preferably adjustable, approximately two time-unit delay line 57 to the input of a blocking oscillator 58. This pulse triggers the blocking oscillator, whereupon the blocking oscillator supplies a pulse of extended duration-preferably greater than ten time-units-through lead 51 to or-circuit 27. The leading edge of the pulse thus supplied through lead 28 to the sum decoder circuit will arrive two time-units later than the pulse through lead 41, and will be coincident with the proper one of the train of pulses supplied through leads 32(0-18) to increase the stored subtotal digit by one. In other Words, when the previously accumulated subtotal digit stored in circuit 40 is zero, and a carry digit is entered in circuit 50, the leading edge of the pulse supplied through lead 28 will be coincident with the pulse supplied to the sum decoder circuit through lead 32(1), the sum decoder circuit will supply a pulse through lead 81(1) to transfer circuit 90, and a signal through lead 91(1) will enter the digit one in circuit 40, thereby increasing the stored augend digit by one, and effectively adding in the desired carry digit. The extended duration of the pulse supplied by blocking oscillator 53 allows it to control the gating of reset pulses, as hereinafter explained, and also insures that lead 23 thus remains energized for a sufficiently long time to rule out the possibility of any subsequent inadvertent -pulse creating a double coincidence at the sume decoder circuit during a single operating cycle.

After successful entry of the new sum digit in the memory of the transfer circuit 9i), a pulse is transmitted through lead 92 to one input lead of an and-gate 59 in the carry entry circuit. The other input lead of andgate 59 is connected to the output of the blocking oscillator 53, and the output lead of and-gate 59 is connected to the reset terminal of flipdlop 55. Thus, once the carry digit stored in ip-liop 55 has been added to the subtotal digit, and the new subtotal digit stored in transfer circuit 9u, flip-dop 55 is cleared to prevent re-addition of the same carry digit in a succeeding operating cycle. On the other hand, receipt of a pulse through lead 92 responsive to the addition of a digit 4from addend entry circuit 7l) will not reset iiip-liop 55, because in this case blo-cking oscillator 53 will not have operated, and there will be no input to the .second lead of and-gate 59.

Reliable operation is assured by the arrangement which makes yit impossible for a pulse to be transmitted through both leads 5l and 52 during the same operating cycle, irrespective of the time of arrival of a carry signal at Hip-flop 55. If a carry is already stored in hip-flop 55 when a pulse reaches and-gate 53 through lead di, then no pulse can be transmitted through and-gate 54 to lead 52 until this carry has been cleared from the flip-liep 55, because delay line 56 insures that the arrival of -a pulse at and-gate 54 is approximately one time-unit later than the arrival of the same pulse at and-gate 53. Because of the two-unit delay in delay line 57, reset pulses received through line 9?., to clear flip-dop 55, always arrive at least one time-unit later than the arrival of -a pulse in the same operating cycle at the left input line of and-gate 54. Hence, under no circumstances will andgate 54 transmit a pulse to line 52 during the same operating cycle that a pulse is transmitted through andgate 53. Under some circumstances a pulse arriving through lead il may be 4transmitted to neither of the lines 5l and 52. This can happen, for example, if a signal arriving through lead 22 enters a carry in iiip-op 55 an instant too late for a pulse from lead il to be transmitted through andgate 53, but before the pulse from lead 41 has arrived at and-gate 543. However, this causes no ditiiculty except the loss of one operating cycle. The next pulse arriving through lead il will be transmitted by and-gate 53, and the carry will be added to the previous subtotal digit.

t is to be noted that the operating speed of ilip-flop 55 does not impose a substantial limitation upon the adding speed of the circuit. The time lag between the arrival of a carry order through lead 22 and the change of state of flip-flop 55 is immaterial. lf the flip-dop has not changed state 'oy the time a pulse from lead il reaches and-gate 54, this pulse will be transmitted through lead 52, so that the addend digit stored in circuit can be added to the subtotal digit. When ilip-op 55 does change state, the next pulse through lead dl will be transmitted by and-gate 53, and the carry will be added to the subtotal digit. However, when the carry has been added, and a reset signal arrives through lead 92, ilip-iiop 55 must reset before the next pulse arrives through lead 4l, in order to insure that the same carry will not be added in twice. This is not a serious limitation upon operating speed, because seven or more time-units will always be available for this reset operation.

Referring now to FIG. 6, the nine-unit delay circuit 60 comprises a delay line 62 having two end terminals and eight taps, equally spaced along its length. This delay line is so designate-d that the time required for a pulse to travel along the line from one of its terminals to the next is exactly equal to one time-unit; thus, the total delay ot a pulse traveling from one end to the other ci line 6?; is nine time-units. These are the same timeunits, all equal to one another, described in connection with the nineteen-unit delay circuit 30. Resistors 63 and ed are connected to the end terminals of delay line 62 and terminate both ends of this delay line in their characteristic impedance, so that there are no substantial reflections of pulses traveling in either direction through the delay line. The ten leads elw-9) are connected in numerical order to successive terminals of delay line 62, beginning at one end of the line. The two input terminals of delay line d2 are connected to the output leads of two and-gates 65 and 66, the and-gate e5 being connected to the same end terminal as lead 61(0), and the, and-gate 66 being connected to the same end terminal as lead 61(9). Lead 52 from circuit 50 is connected to one input lead of each and-gate. The other input leads of and-gates 65 and 66 are connected to a liip-op 67 having one input lead connected to lead 23 for receiving subtract order signals, and having another input lead connected to lead 72, which transmits reset signals from the addend entry circuit, as hereinafter explained. Only one of the and-gates 65 and 66 transmits pulses received from lead 52 at any given time, depending upon the state of dip-flop 67. If a subtract order has not been stored in liip-ilop 67, each pulse received through lead 52 is transmitted through and-gate 65 to the left end of delay line 62, whereupon a pulse appears almost immediately at lead dtml), a pulse appears at lead 61(1) after a delay of one time-unit, a pulse appears at lead 61(2) after a delay of twotime-units, etc. On the other hand, if a subtract order has been stored in hip-Hop 67, each pulse received through lead 52 is transmitted by and-gate 66 to the right end of delay line 62, whereupon a pulse appears at lead 61(9) almost immediately, a pulse appears at lead 61(3) after a delay of one time-unit, a pulse appears at lead 61(7) after a delay of two timeunits, etc.

iter the substraction of a subtrahend digit has been completed, a reset pulse is transmitted through lead 72, which resets flip-flop 67, and thus clears the previously stored subtract order.

Referring to FIG. 7, addend (or subtrahend) digits to be added (or subtracted) are entered through the ten leads 2603-9) connected to input leads of ten hip-flops 73(0-9). ln other words, a zero which is to be added or subtracted is stored in ipdiop 73(0), a one which is to be added or subtracted is stored in flip-liep 73(1), etc. Ten and-gates 74GB-9) each have two input leads, one of which is connected to an output lead of a corresponding one of Hip-flops 73(tl*9), and the other 'of which is connected to the corresponding one of leads 61(6-9) from nine-unit delay circuit 60. The output leads of and-circuits 74(0-9) are connected in common to the input of a blocking oscillator 75.

lf a digit has been stored in one of the ilip-ops 73(0-3), the corresponding and-gate will transmit a pulse from the corresponding one of leads 61(0-9) to trigger blocking oscillator 75. Ii no subtract order has been stored in the memory provisions (flip-hop 67) of the nine-unit delay circuit di), then the delay between the transmission of a pulse through lead 52 to the nine-unit delay circuit and the transmission of a triggering pulse Vto blocking oscillator 75 will be a number of time-units equal to the addend digit stored in iiip-liops 73(0-9). Blocking oscillator 75 is thereupon operated to supply a pulse through lead 71 with a leading edge having -a time position relative to the pulse in lead 52 that is representative of the addend digit which is to be added to the previously stored augend or subtotal digit. It will be remembered that the time position of the pulse through lead 52 is representative of the value of the augend digit, and hence the time position of the leading edge of the pulse provided in lead 7l, relative to the pulse supplied through lead 26 by pulse generator 25, is representative of the sum of the augend and addend digits. In fact, the total delay between the pulse supplied by generator 25 and the leading edge of the pulse supplied through lead 71 by blocking oscillator 75, expressed in the chosen time-units, is one greater than the sum of the augend and addend digits.

The output of blocking oscillator 75 is also connected to one input lead of and-gate 76. The other input lead of and-gate 76 is connected to lead 92 for receiving reset pulses upon the successful entry of a new subtotal digit in transfer circuit 90. The duration of the pulses supplied by blocking oscillator 75 is sufficient that the output pulse of the blocking oscillator is still present at one input lead of and-gate 76 when the reset pulse of the same operating cycle arrives through lead 92. Thus, whenever blocking oscillator 75 has been operated during a particular operating cycle, and the new sum digit has been successfully entered in the transfer circuit 9i), a reset pulse from lead 92 is transmitted through and-gate 75 to reset input leads of the ten flip-flops 73(0-9), for resetting these flip-hops, to clear the stored addend or subtrahend digit. The reset pulse is also transmitted through lead 72 to the reset lead of flip-flop 67 in circuit 60 to clear therefrom the subtract order, if any, stored therein. As further assurance that no more than one pulse per operating cycle will be supplied through lead 71 by the addend entry circuit, the pulses provided by blocking oscillator 75 should have a duration of at least ten time-units. Thus, even if pulses should be transmitted through more than one of the and-gates 74(0-9'), blocking oscillator 75 can not operate more than once in the same cycle.

If a subtrahend digit has been stored in the dip-flops 73(0-9), and concurrently or previously a subtract order was entered in dip-Hop 67 of circuit di), the operation will be exactly the same, except that the pulses transmitted through leads 61(9-9) will be in inverse order to the lead numbers, and the time delay between the pulses transmitted through lead 52 and the leading edge of the pulses transmitted through lead '71 from blocking oscillator 75, measured in time-units, will be equal to nine minus the subtrahend digit. Thus, taking into account the carry entered into the hundredths register and the nine entered into the thousands register concurrently with the entry of a subtract ordr, subtraction is achieved by the addition of the complement of the subtrahend.

For highest reliability, entry of the subtract order through lead 23 should precede entry of the subtrahend digit through leads 20(6-9) slightly, to make sure that the subtrahend digit can in no circumstances be added before the subtract order is entered. With this precaution, the speed of operation of the flip-flops does not substantially limit the speed of addition and subtraction, and the entry of digits to be added and subtracted need not be synchronized with the operation of the adder. It" the digit has not been added in the appropriate tlip-op 73(0-9) in time for one operating cycle, it will simply be added in a subsequent operating cycle. rThere is almost no possibility of error.

The description thus far has explained in detail how a pulse is transmitted through lead 51 to or-circuit 27, if there is a carry from a preceding stage to be added to the previously accumulated subtotal digit, and how a pulse is supplied through lead 71 to or-circuit 27 if there is no carry to be added but there is an addend or subtrahend digit to be added or subtracted stored in the memory provisions of addend entry circuit 70. In either case, the pulse is transmitted by or-circuit 27 through lead 28 to sum decoder circuit 80.

Referring to FIGS. 8A and 8B together, pulses received through lead 28 pass through a differentiating circuit 83, which supplies a relatively short pulse, having a duration less than one time-unit, to lead 84 coincident with the leading edge of the pulse received from lead 2S. The pulse thus supplied to lead 84 will be coincident in time with one of the train of pulses supplied through leads 32(0-18) by the nineteen-unit delay circuit. In fact, the time position of the pulse in lead S4 is such that this pulse is coincident with that one of the train of pulses supplied through leads 32(0-13) that represents the sum of the previously accumulated subtotal or augend digit and either a carry of one, in case a carry has been entered by circuit or the addend digit, in case a digit to be added has been entered by circuit 7i), or nine minus the subtrahend digit, in case a digit to be subtracted has been entered by circuit 7G. In particular, if the required sum is zero, the pulse in lead 84 will be coincident in time with the pulse in lead 32(0); if the required sum is one,

Cil

'i2 the pulse in lead 84 will be coincident in time with the pulse in lead 32(1), etc. The largest sum possible occurs when an addend digit nine is added to an augend digit nine, in which case the sum is eighteen, and the pulse in lead 84 is coincident in time with the pulse in lead 32H8) Nineteen and-gates uddi-ld) have input leads connected to the leads 320i-1S) and other input leads connected in common to lead as illustrated. The output leads of these nineteen and-gates are identified by reference numbers 36(6-18). The function of gates 35(0- is to detect the existence of coincidence between the pulse on lead S4 and any one of the pulses supplied through leads 32(0-8) successively. Hence, gates t:`5(G- 18) are coincidence gates, and when coincidence occurs at any of these gates, a pulse is transmitted to the correspending one of the leads S-51S). With this arrangcment, each time that a pulse appears at lead S having a time position indicative of a desired sum, the pulse is transmitted through the proper and-gate to provide a pulse at the correspondingly numbered one of leads 86(0-13).

Whenever a pulse occurs in any of the leads 36(l@-3), a carry signal should be transmitted to the next following stage; for this purpose, there is provided an or-gate 87 having nine input leads connected to the nine leads 86(ii}18), and an output lead 21 which connects to the carry entry lead of the next stage.

Whenever the sum number is between zero and nine, that number must be transmitted to transfer circuit 90 to be entered in the augend entry circuit as the new subtotal digit. When the sum is between ten and eighteen, the number transmitted to the transfer circuit must be ten less than the sum number. This is accomplished by providing nine or-gates 58(0-8) having first input leads connected to leads 85(9-3), and second input leads connected to leads 8660-18), as illustrated. Leads SMO- 8) are the output leads of these nine or-gates. Lead 81(9) is connected directly to lead 86(9), no or-gate being required in this instance, because there is no lead 36(19). Thus, in every case, an electric pulse is transmitted through the proper one of the nine leads SMG-9) representing the correct new subtotal digit that is to be entered into the augend entry circuit.

Referring now to FIG. 9, lead 81(6) is connected to one input lead of an or-gate 93 having input lead connected to reset order entry lead 24, and having an output lead connected to one input of lipdiop 94(6). Thus, dip-flop 94(0) is set to store the digit zero Whenever a pulse is transmitted either through lead 81(6) or through lead 2d. Leads 81(1-9) are connected to inputs of Hipops 9i(i-9). Thus the ten flip-flops 94(6-9) of the transfer circuit store, in all cases, the proper one of the ten digits zero to nine required to be entered into the augend entry circuit as a new subtotal digit. The proper one of the output leads 91(0-9) continuously transmits an electric signal to the augend entry circuit so long as a digit remains stored in any one of the 'flip-flops 94(0-9).

Or-circuit 95 has ten input leads connected to the ten leads 9It(0-*), and has an output lead connected to trigger a blocking oscillator 95. Thus, whenever any one of the ten dip-flops 9403-9) is set to store a digit, by the receipt of a pulse through lead 2d or one of the leads 31624)), blocking oscillator 95 is triggered, and transmits a reset pulse through lead 92 for clearing the previously stored digit from the memory provisions of augend entry circuit 40, and for clearing either the stored carry from circuit Si) or the stored digit from circuit 70, as hereinbefore explained.

It is again noted that the operating speed of the ipilops is not a material limitation upon the speed of addi- Vtion or subtraction. The circuits of FIGS. 8A and 8B consist solely of and-gates and or-gates, which can be made up entirely of high-speed diodes, as is well known. The ip-ilops shown in FIG. 9 'are not required to operate with exceptional speed. Pulses representing the re- 13 quired sum will continue to be supplied through leads {tlm-9) repeatedly, one in each operating cycle, until this sum is successfully entered in the iiip-liops used for the memory provisions of transfer circuit 9u. When the sum digit is thus entered, a reset pulse will clear the carry, addend, or subtrahend digit.

As has already been explained, the )accumulated subtotal digit is represented substantially continuously by an electric signal appearing in the proper one of leads 42(0-9). This signal can actuate any desired type of readout apparatus. In case nothing more than a visual readout is needed, the readout apparatus can consist merely of ten neon lamps wlw-9), illustrated in FlG. 10. These neon lamps have first electrodes connected to the leads w-9), and second electrodes connected in common to a voltage supply of such Voltage that the only lamp to be lighted is the one connected to that one of leads 42(0-9) presently receiving a signal from circuit 40.

An alternative adder stage is shown in FIG. 1l. In this igure, parts that are identical to parts already described in this specification have been given the same reference numbers for clarity. Pulse genenator periodically supplies pulses through lead llt to a nine-unit delay line lll, provided with ten terminals at which pulses appear successively, at intervals of one time-unit. Leads lime-9) are connected to these ten terminals in inverse order to the order in which pulses appear, i.e., lead ll2(9) is connected to the input end terminal which receives ra pulse almost immediately following transmission of a pulse through lead llii, lead ll2($) is connected to the terminal that receives a pulse one time-unit later, etc., lead 112ml) being connected to the end terminal that receives a pulse after a delay of nine time-units. Leads limit-9) are connected to an augend entry circuit lZtl, illustrated in FlG. l2, and more fully described hereinafter. Following the transmission of each pulse through lead llt) by `a delay expressed in time-units equal to nine minus the stored augend digit, a pulse is transmitted through lead 2d to nineteen-unit delay circuit 3u. Circuit 3u is connected through nineteen leads 32(6)-18) to sum decoder circuit Sil in the manner hereinbefore described. An essential diiference between the arrangement shown in FlG. 11 and the arrangement shown in FIG. 2 is this: with the FIG. 2 arrangement, the pulse transmitted through lead 32(0) follows the initiating pulse supplied by generator 25 with a fixed delay :of one time-unit, whereas in the arrangement shown in FIG. 1l, the pulse transmitted through lead 32m) follows the initiating pulse supplied by generator with a delay expressed in time-units of ten minus the digit stored in the memory provisions of the aug-end entry circuit. ln both cases, the pulses through lead 32(ll-l8) follow the pulses through lead 32() in succession at one time-unit intervals.

Lead ll is connected to the same end terminal of delay line lll as lead M240), and thereby transmits a pulse to amplifier lltnine time-units after the generation of an initiating pulse by generator 25. The delayed pulse is arnplied by amplifier 114 yand transmitted through lead il to carry entry circuit 50, which is connected to or-circuit 27 and delay circuit dit, and through these circuits to addend entry circuit 7u and sum decoder circuit Sil, in the same manner as hereinbefore explained in connection with the arrangement illustrated in FlG. 2. lf there is a carry to be entered, the arrangement shown in FIG. ll supplies a pulse through lead Z3 eleven timeunits after the initiating pulse supplied by generator 25. The pulse supplied through lead 3201i) follows the pulse generated by generator 25 with a delay in time-units equal to ten minus the stored augend digit. Thus, it is evident that the leading edge of the pulse supplied by lead 23 will be coincident with the pulse in that one of the leads 324943) identified by the reference number in parentheses that is one greater than the previously accumulated subtotal or augend digit. From the preceding description of the sum decoder circuit, it will be apparent that this time relation will provide electric signals through the proper one of leads SIW-9), together with a signal through lead 2l if there is to be a carry, for correctly adding the carry from the preceding stage to the previously accumulated subtotal digit. By adding up the time delay in each case, it will be seen that digits entered into circuit t through leads 20(0-9) are also added correctly, or subtracted correctly in case a subtract order entry is also provided through lead 23.

ln the arrangement of FIG. 1l, leads 81(0-9) transmit pulses from the decoder circuit directly to the augend entry circuit 120. When the new subtotal digit is successfully entered into the augend entry circuit, a pulse is provided through the proper one of leads Midi-9) to a printer lid, which prints the new subtotal upon a tape, or performs yany other desired record-making or further operation. Visual readout may be provided Within circuit 126 itself, as hereinafter explained. Leads l21 (0 9) are also connected to ten input leads of an or-circuit 116, which transmits a clear pulse through the two branches of lead 92 to circuits Si) and 79 upon the successful entry of a new augend digit in circuit 120.

Referring now to FIG. l2, augend digits are stored in ten neon lamps l22(tl9) arranged in a circuit such that only one lamp is lit at a time. The ten neon lamps are connected in series with ten diodes 122%(0-9), ten load resistors l2d(l-9), and ya constant-current supply 125, in the manner illustrated. The constant current supply provides a suiiicient current to keep one, and generally only one, of the neon lamps 122(09) lit. Thus, the neon lamps serve both as a memory provision and as a. visual indicator of the stored :augend digit. Ten andgates 12am-9) have first input leads connected to the ten neon lamps l22(tl-9), these leadsbeing connected between each lamp tand its load resistor so that an input is supplied to the and-gate associated with the neon lamp that is lit. Leads ll2(tl-9) connect to the other inputs of the ten and-gates. The outputs of and-gates 1%(0-9) are connected in common to trigger a blocking oscillator 127; thus, the neon lamp that is lit, representing a particular digit stored in the augend entry circuit, determines the time delay between the initiating pulse supplied by generator 215 and the triggering of blocking oscillator 127. As hereinbefore explained, this time delay, expressed in the selected time-units, is equal to nine minus tie stored augend digit. Preferably, the duration of the pulse generated by blocking oscillator 127 is at least ten time-units, so that the blocking oscillator can be triggered no more than once in an operating cycle, even if two or more of the neon lamps 12209-9) should inadvertently become lit concurrently. A dilferentiator 128 supplies a relatively short pulse having a duration less than one time unit to lead 26, concurrent with the leading edge of the pulse generated by the blocking oscillator 127.

Leads hlm-9) from circuit 39 are connected to trigger ten blocking oscillators MMG-9). The outputs of these ten blocking oscillators are connected to the ten neon lamps lZZw-) between the lamp and the diode, as shown. The polarity of the diodes illustrated assumes that the blocking oscillators will supply negative pulses; if the blocking oscillators supplied positive pulses, the polarity of the diodes would be reversed. The polarity of supply is such that current flows in the easy direction through the ten diodes. When any one of the blocking oscillators 1255*(0-9) is triggered, it generates a pulse that increases the voltage across the corresponding one of the ten neon lamps l22(il9). This lights that lamp, and the resulting surge of current decreases the voltage across the other lamps, and extinguishes any previously lit lamps. ln this way, the proper lamp is lit, and all other lamps are extinguished, whenever any one of the ten blocking oscillators HWG-9) is triggered to enter a new subtotal digit in the augend entry circuit. It should be noted that 15 the lighting and unlighting of lamps required for entry of a new digit need not be completed in one unit of time. The output pulses of the blocking oscillators may have a duration as long as is required to enter new digits in the neon lamp memory with high reliability.

Output pulses from the blocking oscillators also supply pulses through leads RMU-9) for operating printer 115, and for sending reset pulses through or-circuit 116 and lead 92 to circuits Si) and 70.

The reset lead 24 is connected as shown to lamp rif/.2(0)

through a diode 123;(R). Thus, a negative pulse of adequate amplitude and duration supplied through lead 24 will light lamp l22(i)) and extinguish all the other lamps, in the same manner as the action of blocking o cillator .129(6).

' It will be understood that the invention in its broader aspects is not limited to the specific embodiments illustrated and described, and that various changes and modifications will be apparent to those skilled in the art.

What is claimed is:

l. An arithmetic circuit comprising first memory means for storing a number, second memory means for storing another number, means for entering a plurality of such numbers successively into storage within said memory means, means for producing an electric pulse, means for producing a train of electric pulses, first coincidence means, means connected and arranged to compare the result of an arithmetic operation involving the two stored numbers in said first and second memory means with one of said train of pulses to produce an output pulse having a time position with respect to the first pulse of said train of pulses related to said result, second coincidence means connected and arranged to compare the time position or said output pulse relative to the first pulse of said train of pulses for determining the numerical value of the result, means interconnecting said second coincidence means and said first memory means for automatically changing the number stored within the first memory means to the sodetermined value, and means interconnecting said second coincidence means and said second memory means for automatically removing the then-stored number from storage within the second memory means upon the completion of such determination.

2. An adding circuit comprising the combination of first memory means for storing a number, second memory means for storing another number, means for entering a plurality of numbers successively into storage within said memory means, a tapped delay line having an input terminal connected to receive a first pulse and having a plurality of output terminals arranged to provide a train of pulses following one another at fixed time intervals following the receipt of said rst pulse, first coincidence means connected and arranged to compare the contents of said first and second memory means with one of said chain of pulses to provide a second electric pulse separated from said first pulse by a time interval determined by the algebraic sum of the two stored numbers, a plurality of coincidence gates each having a first input connection to an output terminal of said delay line and having a second input connection arranged to receive the second pulse, so that a coincidence of pulses occurs at only one coincidence gate determined by the algebraic sum of the stored numbers, means interconnecting said coincidence gates and said first memory means for automatically changing the number stored within the first memory means to equality with the algebraic sum represented by such coincidence of pulses, and means interconnecting said coincidence gates and said second memory means for automatically removing the then-stored number from storage within the second memory means responsive to the occurrence of such coincidence of pulses.

3. An addition-subtraction circuit comprising electrical first memory means for storing a numerical value representing at least a portion of an `accumulated subtotal, electrical second memory means for storing a numerical value aisance l@ representing at least a portion of an addcnd-subtrahend number, parallel input electric leads for entering a plurality of such numerical values successively into said second memory means, electrical third memory means for storing subtract orders, a subtract order input lead for entering such orders into said third memory means, electrical fourth memory means for storing a carry, a carry input lead for entering carries into said fourth memory means, first pulse-producing means for producing an electric plus means connected to said first pulse-producing means for producing a train of electric pulses spaced at equal one-unit time intervals following receipt of said first pulse in response to a pulse from said first pulse-producing means, rst coincidence means connected and arranged to compare the contents of said first memory means producing a rst output pulse having a time position relative to the beginning of said train of pulses of a time equal to a first variable time less a fixed time, said first variable time being a number of one-unit time intervals equal to the numerical value stored within said first memory means, first delay means providing a fixed delay, second delay means providing a delay one time-unit greater than that provided by said second delay means, a first switching means connected to and controlled by said fourth memory means and arranged to route the firstmentioned pulse through said second delay means or through said first delay means, selectively, depending upon whether or not a carry is stored within said third memory means, fourth delay means including a delay line having delay-line input terminals at its opposite ends, second switching means connected to and controlled by said third memory means and arranged to route pulses from said first delay means to one of said delay line input terminals or the other, selectively depending upon whether or not a subtract order is stored within said third memory means, said third delay means being connected to and controlled by said second memory means and arranged to delay pulses supplied to said one delay-line input terminal when there is a stored subtract order by a number of one-unit time intervals equal to a number one smaller than the radix of the number system employed minus the numerical value stored within said second memory means, and to delay pulses supplied to said other delay-line input terminal when there is no stored subtract order by a number or" one-unit time intervals equal to the numerical value stored within said second memory means, a plurality of two-input coincidence gates, one of said inputs of each such gate connected and arranged to receive successively the successive pulses of said train, means for supplying to the other input of all of said coincidence gates simultaneously the deiayed pulses transmitted from said second and third delay means, whereby there is a coincidence of pulses at only one coincidence gate representing an algebraic sum having a numerical value equal to the value stored within the first memory means, plus one if there is a carry stored Within the fourth memory means, or plus a number one smaller than the radix minus the value stored within the second memory means if there is no stored carry but there is a subtract order stored within the third memory means, or plus the value stored within the second memory means if there is neither a stored carry nor a stored subtract order, means for changing the value stored in the rst memory means to a value equal to said sum if said sum is less than the radix of the number system employed, or equal to said sum minus the radix if said sum is not less than the radix, a carry output lead, means for supplying an electric pulse to said carry output lead if said sum is larger than the radii: minus one, means for automatically clearing the stored number from said second memory means after the addition of an addend, means for automatically clearing the stored number from said second memory means and the subtract order from said third memory means after subtraction of a subtrahend, and means for automatically clearing the carry 17 from said fourth memory means after the addition of a carry.

4. A multi-stage adder-subtractor comprising a plurality of circuits each comprising; electrical iirst memory means for storing a numerical value representing at least a portion of an accumulated subtotal, electrical second memory means for storing a numerical value representing at least a portion of an addend-subtrahend number, parallel input electric leads for entering a plurality of such numerical values successively into said second memory means, electrical third memory means for storing subtract orders, a subtract order input lead for entering such orders into said third memory means, electrical fourth memory means for storing a carry, a carry input lead for entering carries into said fourth memory means, first pulse-producing means for producing an electric pulse, means connected to said first pulse-producing means for producing a train of electric pulses spaced at equal one-unit time intervals following receipt of said rst pulse in response to a pulse from said irst pulse-producing means, first coincidence means connected and arranged to compare the contents of said first memory means producing a first output pulse having a time position relative to the beginning of said train of pulses of a time equal to a first variable time less a fixed time, said first variable time being a number of one-unit time intervals equal to the numerical value stored within said first memory means, first delay means providing a fixed delay, second delay means providing a delay one time-unit greater than that provided by said second delay means, a first switching means connected to and controlled by said fourth memory means and arranged to route the first-mentioned pulses through said second delay means or through said first delay means, selectively, depending upon whether or not a carry is stored within said third memory means, fourth delay means including a delay line having delay-line input terminals at its opposite ends, second switching means connected to and controlled by said third memory means and arranged to route pulses from said first delay means to one of said delay-line input terminals or the other, selectively, depending upon whether or not a subtract order is stored within said third memory means, said third delay means being connected to and controlled by said second memory means and arranged to delay pulses supplied to said one delay-line input terminal when there is a stored subtract order by a number of one-unit time intervals equal to a number one smaller than the radix of the number system employed minus the numerical value stored within said second memory means, and to delay pulses supplied to said other delay-line input terminal when there is no stored subtract order by a number of one-unit time intervals equal to the numerical value stored Within said second memory means, a plurality of two-input coincidence gates, one of said inputs of each said gate connected and arranged to receive successively the successive pulses of said train, means for supplying to the other input of all of said coincidence gates simultaneously the delayed pulses transmitted from said second and third delay means, whereby there is a coincidence of pulses at only one coincidence gate representing an algebraic sum having a numerical value equal to the value stored within the first memory means, plus one if there is a carry stored within the fourth memory means, or plus a number `one smaller than the radix minus the value stored within the second memory means if there is no stored carry but there is a subtract order stored within the third memory means, or plus the value stored within the second memory means if there is neither a stored carry nor a stored subtract order, means for changing the value stored in the first memory means to a value equal to said sum if said sum is less than the radix of the number system employed, or equal to said sum minus the radix if said sum is not less than the radix, a carry output lead, means for supplying an electric pulse to said carry output lead if said sum is larger than the radix minus one, means for automatically clearing the stored number from said second memory means after the addition of an addend, means for automatically clearing the stored number from said second memory means and the subtract order from said third memory means after subtraction of a subtrahend, and means for automatically clearing the carry from said fourth memory means after the addition of a carry; connections from the carry output lead of each of such circuits except the last to the carry input lead of the next following one of such circuits; and connections for entering carry orders in parallel through the subtract order entry leads of all such circuits except the last, the carry input lead of the first such circuit, and the parallel input electric lead for entering a numerical value one smaller than the radix in the last such circuit.

5. A circuit for adding two numbers in va number system of radix N, comprising first memory means for storing a number A having a numercial value between zero and N-l, second memory means for storing a number B having a numerical value between zero and N-l, a rst plurality of two-input and-gates, one input of each connected to 4said first memory means so that only one such gate, determined by the stored number A, will conduct electric pulses transmitted to the other input, a pulse generator, a first delay-line means having .an input terminal connected to receive pulses from said generator, said first delay-line means having 4a plurality of output terminals arranged and connected to supply electric pulses to the andagates of said first plurality successively at one-unit time intervals following the receipt of a pulse from said generator, whereby the period of time between the receipt of a pulse from said generator land transmission of such a pulse by one of the first plurality of and-gates is representative of the stored number A, a second plurality of two-input land-gates, one input of each connected `to said second memory means so that -only one such gate, determined by the stored number B, will conduct electric pulses transmitted to the other input, a second delay-line means having an input terminal connected Ito receive pulses transmitted by said first plurality of and-gates, said second delay-line means having a plurality of output terminals arranged and connected to supply electric pulses to the andgates of said second plurality successively at one-unit time intervals, whereby the period of time between recept of a pulse from said first plurality of and-gates and transmission of `such a pulse by the second plurality of and-gates is representative of the algebraic sum of the stored numbers A `and B, .and a plurality of coincidence gates connected to receive the pulses transmitted by said second plurality of and-gates, means for supplying electric pulses to said coincidence gates successively at one-unit time intervals following the receipt of a pulse from said generator, whereby a coincidence of pulses occurs at only one coincidence gate determined by the :algebraic sum of A and B, means for combining pulses transmitted by pairs of coincidence gates representing algebraic sums that differ by an ramount equal to the radix N, said combining means connected between the out-puts yof each of the two gates of said pairs of coincidence gates, means for changing the value stored in the first memory means to a value equal to said sum if said sum is less than the radix of the number system employed, or equal to said sum minus the radix if said Asum is not less lthan the radix, 4and means for automatically clearing the stored number from said second memory means after the addition of the number B.

6. A circuit as in claim 5, additionally comprising means for supplying a pulse representing a carry to a following stage Whenever a coincidence of pulses occurs at a gate representing an algeraic sum larger than N-l, third memory means for storing a carry from a preceding stage, switching means connected between said first plurality of `and-gates and second delay-line means, and third delay-line means connected between said switching means and said coincidence gates, said switching means being connected to and controlled by said third memory means and said switching means being connected and arranged to transmit pulses from said first plurality of and-gates to said second delay-line means when there is no stored carry, and through said third delay-line means to said coincidence gates when there is a stored carry.

7. A circuit as in claim 5, wherein said second delayline means has input terminals at opposite ends thereof, additionally comprising switching means for supplying the pulses transmitted from the first plurality of and-gates to the input terminal at one end of the second delay-line means when the number B is to be added, and for supplying such pulses to the input terminal at the opposite end of the second delay-line means when the number B is to be subtracted.

8. A circuit for adding two numbers in a number system of radix N, comprising first memory means for storing a number A having a numerical value between zero and N-l, second memory means for storing a numerical value between zero and N-l, a rst plurality of two-input and-gates, one input of each connected to said first memory means so that only one such gate, determined by the stored number A, will conduct electric pulses transmitted to the other input, a pulse generator, tirst delay-line means having an input terminal connected to receive pulses from said generator, said first delay-line means having a plurality of output terminals arranged and connected to supply electric pulses `to the and-gates of said first plurality successively at one-unit time intervals following the receipt of a pulse from said generator, whereby the period of time between the receipt of a pulse from said generator and transmission of such a pulse by one of the first plurality of and-gates is representative of the stored number A, a second plurality of two-input and-gates, one input of each connected to said second memory means so that only one such gate, determined by the stored number B, will conduct electric pulses transmitted to the other input, second delay-line means having an input terminal arranged and connected to receive pulses in fixed time relation to the pulses supplied by said generator, said second delay-line means having a plurality of output terminals arranged and connected to supply electric pulses to the and-gates of said second plurality successively at oneunit time intervals, whereby the period of time between receipt of a pulse from said generator and transmission of such a pulse by the second plurality of and-gates is representative of the stored number B, the combined time interval between the transmission of a pulse by said generator and transmission of a pulse by said lirst plurality of and-gates, and between the transmission of a pulse by said generator `and the transmission of a pulse by the second plurality of and-gates being representative of the algebraic sum of A and B, a plurality of coincidence gates connected to receive the pulse transmitted by said second plurality of and-gates, means for supplying electric pulses to said coincidence gates successively at one-unit time intervals following the transmission of a pulse by said first plurality of and-gates, whereby a coincidence of pulses occurs at only one coincidence gate determined by the algebraic sum of A and B, means for combining pulses transmitted yby pairs of coincidence gates representing algebraic sums that diifer by an amount equal to the radix N, said combining means connected between the outputs of each of the two gates of said pairs of coincidence gates, means for changing the value stored in the rst memory means to 4a value equal to said sum if said sum is less than the radix of the number, or equal to said sum minus the radix if said sum is not less than the radix, and means for automatically clearing the stored number from said second memory means after the addition of the number B.

9. A circuit as in claim 8, additionally comprising means for supplying a pulse representing a carry to a following stage whenever a coincidence of pulses occurs at a gate representing an algebraic sum larger than N-l, third memory means for storing a carry from a preceding stage, switching means connected ahead of the input terminal to said second delay-line means, and third delayline means connected between said switching means and said coincidence gates, said switching means being connected to and controlled by `said third memory means, and said switching means being connected and arranged to transmit pulses to said second delay-line means when there is no stored carry, and through said third delay-line means to said third coincidence gate when there is a stored carry.

l0. A circuit as in claim 8, wherein said second delayline means has input terminals at opposite cnds thereof, additionally comprising switching means for supplying pulses to the input terminal at one end of the second delayline means when the number B is to be added, and for supplying such pulses to the input terminal at the opposite end of the second delay-line means when the number B is to be subtracted.

References Cited in the le of this patent UNITED STATES PATENTS 

1. AN ARITHMETIC CIRCUIT COMPRISING FIRST MEMORY MEANS FOR STORING A NUMBER, SECOND MEMORY MEANS FOR STORING ANOTHER NUMBER, MEANS FOR ENTERING A PLURALITY OF SUCH NUMBERS SUCCESSIVELY INTO STORAGE WITHIN SAID MEMORY MEANS, MEANS FOR PRODUCING AN ELECTRIC PULSE, MEANS FOR PRODUCING A TRAIN OF ELECTRIC PULSES, FIRST COINCIDENCE MEANS, MEANS CONNECTED AND ARRANGED TO COMPARE THE RESULT OF AN ARITHMETIC OPERATION INVOLVING THE TWO STORED NUMBERS IN SAID FIRST AND SECOND MEMORY MEANS WITH ONE OF SAID TRAIN OF PULSES TO PRODUCE AN OUTPUT PULSE HAVING A TIME POSITION WITH RESPECT TO THE FIRST PULSE OF SAID TRAIN OF PULSES RELATED TO SAID RESULT, SECOND COINCIDENCE MEANS CONNECTED AND ARRANGED TO COMPARE THE TIME POSITION OF SAID OUTPUT PULSE RELATIVE TO THE FIRST PULSE OF SAID TRAIN OF PULSES FOR DETERMINING THE NUMERICAL VALUE OF THE RESULT, MEANS INTERCONNECTING SAID SECOND COINCIDENCE MEANS AND SAID FIRST MEMORY MEANS FOR AUTOMATICALLY CHANGING THE NUMBER STORED WITHIN THE FIRST MEMORY MEANS TO THE SODETERMINED VALUE, AND MEANS INTERCONNECTING SAID SECOND COINCIDENCE MEANS AND SAID SECOND MEMORY MEANS FOR AUTOMATICALLY REMOVING THE THEN-STORED NUMBER FROM STORAGE WITHIN THE SECOND MEMORY MEANS UPON THE COMPLETION OF SUCH DETERMINATION. 